This application claims the priority of German patent document 100 38 912.0, filed Aug. 9, 2000, the disclosure of which is expressly incorporated by reference herein.
The invention relates to a method of correcting the position of moving targets in synthetic aperture radar (SAR) images.
In principle, SAR-images are range Doppler matrices in which the position of fixed targets in the range direction is determined by means of the signal transit time, and the azimuthal position is determined by means of the Doppler frequency from single-channel or multi-channel range/Doppler measurement data.
To improve the detection of moving targets in SAR-images, it is necessary to suppress both interference and signals which originate from fixed targets. A suitable method for this purpose is known as Space-Time Adaptive Processing (STAP). In such known methods for this purpose, the raw radar data are, as a rule, filtered in the time domain (xe2x80x9cSpecial Issue on Space-Time Adaptive Processing (STAP)xe2x80x9d, Electronics and Communication Engineering Journal, Volume 11, 1999, February, No. 1, ISSN 0954-0695). However, the determination of the filtering coefficients and the filtering in the time domain require very high computing expenditures.
In German Patent Documents DE 100 12 411 and DE 100 35 530, which are not prior publications, methods are introduced in which the determination of STAP filtering coefficients and the STAP filtering take place in the frequency domain so that the number of computing operations per matrix element is limited to a few.
The positions of targets in the azimuthal direction resulting from the SAR-processing apply only to fixed targets because, in the case of moving targets, the measured Doppler frequency is falsified due to the component of vehicle movement in the range direction. For this reason, moving targets are imaged in the SAR-image at a wrong azimuth position, absent further signal processing.
In order to correct such a falsified image, multi-channel range/Doppler measurement data are normally used, so as to permit a repositioning in the azimuthal direction by the evaluation of the transit time differences in the individual data channels. As a rule, the well-known monopulse mode or computation-intensive correlation processes are used for this purpose which are described in the relevant technical literature.
It is an object of the present invention to provide an improved method of repositioning moving targets in SAR-images which consist of multi-channel range/Doppler measurement data X with NDZ Doppler resolution cells.
This and other objects and advantages are achieved by the method according to the invention, which advantageously permits the repositioning of moving targets in SAR-images. Based on filtering coefficients xcex1 and xcex2 of the STAP which are transformed into the frequency domain, on the one hand, a family of NDZ pattern functions M is defined and, on the other hand, in combination with the multi-channel range/Doppler measurement data, a testing function T is defined. On this basis, a correlation function K is then generated which corresponds to the correlation of a testing function T with a selected function of the family of pattern functions M. Subsequently, in a manner according to the invention, the true azimuth position of a moving target can be computed on the basis of the position of maximum of this correlation function K. According to method of the invention, those STAP filtering coefficients can, for example, be used which are defined by means of the methods described in German Patent Documents DE 100 12 411 and DE 100 35 530, referred to previously.
The determination of the filtering coefficients xcex1(i) and xcex2(i) of the STAP filter, according to the method described in DE 100 35 530 and DE 100 12 411, will be discussed hereinafter.
In this case, X1 (i,j) and X2 (i,j) exist with 1xe2x89xa6jxe2x89xa6NRG, wherein X1 (i,j) is the complex range/Doppler matrix of the first channel (for example, L or xcexa3) of the coherent radar system, and X2 (i,j) is the complex range/Doppler matrix of the second channel (for example, R or xcex94). Furthermore, NDZ is the number of Doppler Cells and NRG is the number of range gates (distance gates).
First, the auto- and cross-correlations of both input channels are determined according to Equation 1 to 3. Here, r11 indicates the auto-correlation of the first channel; r22 indicates the auto-correlation of the second channel, and r12 indicates the cross-correlation of both channels.                                           r            11                    ⁡                      (            i            )                          =                              ∑                          j              -              1                                      N              RG                                ⁢                      xe2x80x83                    ⁢                                                    X                1                            ⁡                              (                                  i                  ,                  j                                )                                      ·                                          X                1                *                            ⁡                              (                                  i                  ,                  j                                )                                                                        Equation        ⁢                  xe2x80x83                ⁢        1                                                      r            22                    ⁡                      (            i            )                          =                              ∑                          j              =              1                                      N              RG                                ⁢                      xe2x80x83                    ⁢                                                    X                2                            ⁡                              (                                  i                  ,                  j                                )                                      ·                                          X                2                *                            ⁡                              (                                  i                  ,                  j                                )                                                                        Equation        ⁢                  xe2x80x83                ⁢        2                                                      r            12                    ⁡                      (            i            )                          =                              ∑                          j              =              1                                      N              RG                                ⁢                      xe2x80x83                    ⁢                                                    X                1                            ⁡                              (                                  i                  ,                  j                                )                                      ·                                          X                2                *                            ⁡                              (                                  i                  ,                  j                                )                                                                        Equation        ⁢                  xe2x80x83                ⁢        3            
with 1xe2x89xa6ixe2x89xa6NDZ.
The values of the auto- or cross-correlations determined from the two input channels may be subjected to an additional processing before the determination of the filtering coefficients xcex1(i) and xcex2(i) of the STAP filter.
In this case, it is, for example, possible to determine which of the two channels has the better signal-to-noise ratio (S/N). A possible method for this purpose is indicated in Equation 4.                                           max            ⁡                          (                                                                    r                    11                                    ⁡                                      (                    i                    )                                                  ❘                                  1                  ≤                  i                  ≤                                      N                    DZ                                                              )                                                          ∑                              i                =                1                                            N                DZ                                      ⁢                          xe2x80x83                        ⁢                                          r                11                            ⁡                              (                f                )                                                     greater than                               max            (                                                            r                  22                                ⁡                                  (                  i                  )                                            ❘                              1                ≤                i                ≤                                  N                  DZ                                                                                        ∑                              i                =                1                                            N                DZ                                      ⁢                          xe2x80x83                        ⁢                                          r                22                            ⁡                              (                f                )                                                                        Equation        ⁢                  xe2x80x83                ⁢        4            
If this equation is true, the first channel (corresponding to {overscore (X)}1 with r11) has a better signal-to-noise ratio; otherwise, the second channel (corresponding {overscore (X)}2 with r22).
Following this determination as a function of the two channels {overscore (X)}1 and {overscore (X)}2 has a better signal-to-noise ratio (S/N), a defined pair of equations can be used to determine the filtering coefficient xcex1(i) and xcex2(i) of the STAP filter. In this case, the selection rule is designed such that, in the event that the channel {overscore (X)}1 has a better signal-to-noise ratio (S/N) , the apir of the Equations 5 and 6 is selected, but otherwise, the pair of the Equations 7 and 8 is selected.
a(i)=xe2x88x92(21+1)xe2x80x83xe2x80x83Equation 5                              b          ⁡                      (            i            )                          =                              ∑                          k              =                                                N                  DZ                                -                1                                                                    N                DZ                            +              1                                ⁢                      xe2x80x83                    ⁢                                                    r                12                            ⁡                              (                                                                            (                                              i                        +                        k                        -                        1                                            )                                        ⁢                    mod                    ⁢                                          xe2x80x83                                        ⁢                                          N                      DZ                                                        +                  1                                )                                                                    r                22                            ⁡                              (                                                                            (                                              i                        +                        k                        -                        1                                            )                                        ⁢                    mod                    ⁢                                          xe2x80x83                                        ⁢                                          N                      DZ                                                        +                  1                                )                                                                        Equation        ⁢                  xe2x80x83                ⁢        6            
for 1xe2x89xa6ixe2x89xa6NDZ, and l=0, 1, 2, . . . ;                               a          ⁡                      (            i            )                          =                              ∑                          k              =                                                N                  DZ                                -                1                                                                    N                DZ                            +              1                                ⁢                      xe2x80x83                    ⁢                                                    r                12                *                            ⁡                              (                                                                            (                                              i                        +                        k                        -                        1                                            )                                        ⁢                    mod                    ⁢                                          xe2x80x83                                        ⁢                                          N                      DZ                                                        +                  1                                )                                                                    r                11                            ⁡                              (                                                                            (                                              i                        +                        k                        -                        1                                            )                                        ⁢                    mod                    ⁢                                          xe2x80x83                                        ⁢                                          N                      DZ                                                        +                  1                                )                                                                        Equation        ⁢                  xe2x80x83                ⁢        7            
b(i)=xe2x88x925xe2x80x83xe2x80x83Equation 8
for 1xe2x89xa6ixe2x89xa6NDZ, and l=0, 1, 2, . . . ;
According to Equations 6, 7 the mean value of the correlation values of 21+1 adjacent Doppler cells are used to determine the filtering coefficient a(i), b(i). However, 1=0 is also possible, i.e., only the correlation values of one Doppler cell (Doppler cell i) are taken into account.
After the determination the filter coefficients xcex1(i) and xcex2(i) are subjected to a scaling.                               α          ⁡                      (            i            )                          =                              a            ⁡                          (              i              )                                                                                            a                  ⁡                                      (                    i                    )                                                  ·                                                      a                    *                                    ⁡                                      (                    i                    )                                                              +                                                b                  ⁡                                      (                    i                    )                                                  ·                                                      b                    *                                    ⁡                                      (                    i                    )                                                                                                          Equation        ⁢                  xe2x80x83                ⁢        9                                          β          ⁡                      (            i            )                          =                              b            ⁡                          (              i              )                                                                                            a                  ⁡                                      (                    i                    )                                                  ·                                                      a                    *                                    ⁡                                      (                    i                    )                                                              +                                                b                  ⁡                                      (                    i                    )                                                  ·                                                      b                    *                                    ⁡                                      (                    i                    )                                                                                                          Equation        ⁢                  xe2x80x83                ⁢        10            
with 1xe2x89xa6ixe2x89xa6NDZ.
These coefficients xcex1(i) and xcex2(i) are the basis of a further processing according to the invention, which will be described hereinafter.
Other objects, advantages and novel features of the present invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.